Blender 2.9.1 Boolean Modifer Union
The zappy looking face on the close side indicates a face in the same location. Are you using the Boolean Modifier on the cone with the cube as a separate object? If so, I highly recommend having the two as one mesh object and using the edit mode Boolean operation instead. To fix the situation you have without doing this, apply the modifier on the cone, then delete the cube: The cone’s current modifier-added geometry is identical to but not the same thing as the cube and is overlapping it.